Computing permanents over fields of characteristic 3: where and why it becomes difficult

Author(s):  
G. Kogan
Keyword(s):  
1997 ◽  
Vol 195 (1) ◽  
pp. 30-73
Author(s):  
Panagiotis Papadopoulos
Keyword(s):  

Author(s):  
D. F. Holt ◽  
N. Spaltenstein

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.


2019 ◽  
Vol 18 (04) ◽  
pp. 1950069
Author(s):  
Qian Liu ◽  
Yujuan Sun

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are partially settled, where [Formula: see text] is a positive integer.


2005 ◽  
Vol 86 (2) ◽  
pp. 491-499 ◽  
Author(s):  
Peter Revill ◽  
Xuan Trinh ◽  
James Dale ◽  
Rob Harding

Sequencing of the monopartite RNA genome of a Fijian isolate of Taro vein chlorosis virus (TaVCV) confirmed that it is a definitive rhabdovirus with most similarity to members of the genus Nucleorhabdovirus. The TaVCV 12 020 nt negative-sense RNA genome contained six ORFs in the antigenomic sequence, equivalent to the N, P, 3, M, G and L genes that have been identified in other rhabdoviruses. The putative gene products had highest similarity to those of the nucleorhabdovirus Maize mosaic virus. A characteristic 3′-AAUUCUUUUUGGGUUGU/A-5′ sequence was identified in each of the intergenic regions and the TaVCV leader and trailer sequences comprised 140 and 61 nt, respectively. Assignment of TaVCV to the genus Nucleorhabdovirus was supported by thin-section electron microscopy of TaVCV-infected taro leaves, which identified virions budding from nuclear membranes into the perinuclear space. Variability studies identified high levels of TaVCV sequence diversity. Within the L gene of 20 TaVCV isolates from Fiji, the Federated States of Micronesia, New Caledonia, Papua New Guinea, Solomon Islands and Vanuatu, maximum variability at the nucleotide level was 27·4 %. Within the N gene, maximum variability among 15 isolates at the nucleotide level was 19·3 %. The high level of TaVCV variability observed suggested that the introduction of TaVCV to the Pacific Islands was not a recent occurrence.


2005 ◽  
Vol 48 (3) ◽  
pp. 428-444
Author(s):  
Roland Miyamoto ◽  
Jaap Top

AbstractWe determine conductor exponent, minimal discriminant and fibre type for elliptic curves over discrete valued fields of equal characteristic 3. Along the same lines, partial results are obtained in equal characteristic 2.


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